To: Peter Eisentraut <peter_e@gmx.net>
cc: "He Weiping(Laser Henry)" <laser@zhengmai.com.cn>,
	pgsql-docs@postgresql.org
Subject: Re: some errors and/or bugs? 
In-reply-to: <Pine.LNX.4.30.0012191732170.1000-100000@peter.localdomain> 
References: <Pine.LNX.4.30.0012191732170.1000-100000@peter.localdomain>
Comments: In-reply-to Peter Eisentraut <peter_e@gmx.net>
	message dated "Tue, 19 Dec 2000 17:36:37 +0100"
Date: Wed, 20 Dec 2000 14:35:44 -0500
Message-ID: <10051.977340944@sss.pgh.pa.us>
From: Tom Lane <tgl@sss.pgh.pa.us>

Peter Eisentraut <peter_e@gmx.net> writes:
> Tom Lane writes:
>> It's correct, if the underlying float arithmetic is IEEE-compliant.
>> Rounding for exact half-integral values is supposed to be "round to
>> nearest even".  So 42.5 goes to 42, but 43.5 goes to 44.
>> 
>> I notice our NUMERIC rounding code does not do that ... perhaps it
>> should.

> More precisely, an IEEE-compliant system would offer the choice of
> rounding up, rounding down, rounding toward zero, or rounding toward even.
> I would guess that the default is merely the potentially best performing.

Hmm.  Round-toward-even is preferred by numerical analysts on the theory
that it introduces less systematic bias than simpler rounding rules.
(If you always round half-integral values in the same direction, then
your results are slightly biased, just as if you'd set the up/down split
point at say 0.4 instead of 0.5.)  However this theory only holds if you
assume an imprecise starting value.  That's a reasonable assumption for
float arithmetic, but not so reasonable for type numeric.

> We could offer these options (much more easily) for the numeric case, but
> since numeric is very often used for business type applications, the
> customary rounding method (up) should be preferred.

You're probably right, we shouldn't change it.

			regards, tom lane